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3 years ago

Given the following PARALLELOGRAM, find the measure of each angle below.

Mathematics

1 answer:

vladimir1956 [14]3 years ago

6 0

Answer:

m∠BEC = 65°

m∠DEC = 115°

m∠DAE = 78°

m∠ECD = 40°

m∠BAD = 118°

m∠ADC = 62°

Step-by-step explanation:

m∠BEC = 65°

Opposite angles formed by intersecting lines are congruent

m∠DEC = 180 - 65 = 115°

A straight line has a degree measure of 180

m∠DAE = 78°

Opposite interior angles of two parallel lines cut by a transversal are congruent

m∠ECD = 180 - [m∠DEC + 25] = 40°

Sum of angles inside triangle ECD has a measure of 180

m∠BAD = 78 + m∠ECD = 118°

Opposite angles of a parallelogram are congruent

2(m∠BAD) + 2(m∠ADC) = 360

118 + m∠ADC = 180

m∠ADC = 62°

Sum of angles inside a parallelogram = 360°

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A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performa

ss7ja [257]

Answer:

x = number of tickets sold for $26 = 3900 tickets

y = number of tickets sold for $40 = 2100 tickets

Step-by-step explanation:

A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $185,400?

Let

x = number of tickets sold for $26

y = number of tickets sold for $40

x + y = 6000

x = 6000 - y

$26 × x + $40 × y= $185, 400

26x + 40y = 185400

Substitute

26(6000 - y) + 40y = 185400

156000 - 26y + 40y = 185400

Collect like terms

- 26y + 40y = 185400 - 156000

14y = 29400

y = 29400/14

y = 2100 tickets

x = 6000 - y

x = 6000 - 2100

x = 3900 tickets

Hence

x = number of tickets sold for $26 = 3900 tickets

y = number of tickets sold for $40 = 2100 tickets

5 0

3 years ago

Anyoneee help im stuck !! 15 points!!

Gnom [1K]

Answer:

Given: $\angle 1$ , $\angle 2$ , $\angle 3$ , $\angle 4$ formed by two intersecting segments.

In the given figure;

Linear pair states that a pair adjacent angle formed when two lines intersect.

Then by definition of linear pairs,

$\angle 1$ and $\angle 2$ forms a linear pair

Also, $\angle 2$ and $\angle 3$ forms a linear pair.

Linear pair postulates states that the two angle that forms a linear pair are supplementary(i,e add up to 180 degree).

Then by linear pair postulates;

$m\angle 1+ m\angle 2 =180^{\circ}$

and

$m\angle 2+m \angle 3 =180^{\circ}$

Substitution property of equality states that if x =y then, x can be substituted in for y or vice -versa.

then by substitution property of equality:

$m\angle 1+m\angle 2=m\angle 2+ m\angle 3$

Addition property of equality states that:

if x =y, then x + z = y+ z

By addition property of equality:

$m\angle 1 =m\angle 3$ hence proved!

6 0

3 years ago

Which of the following relations is NOT a function?

topjm [15]

According to Wikipedia: "<span>In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output."

So based of this we need to look for a set where one of the x values or the y values is the same, and the other number is different.

Answer:
B.
(1,4) and (1,1) both have the same x, but different y!
</span>

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4 years ago

Simplify the expression. A) 8^4•8^9

OlgaM077 [116]

Answer:

${8}^{13}$

Step-by-step explanation:

${8}^{4} \times {8}^{9} \\ {8}^{4 + 9} \\ {8}^{13} \\ = 5.497558139 \times 10 ^{11}$

Hope this helps you.

Let me know if you have any other questions :-)

7 0

3 years ago

How to divide 4.48 ÷7

Rina8888 [55]

Answer:

Step-by-step explanation:

4.48/7

7 into 4 (0 times)

Bring next number down 4.48 ⬇️

7 into 44 (6 times, 2 left over)

Bring next number down 4.48 ⬇️

7 into 28 (4 times)

Answer 0.64

I'm always happy to help :)

5 0

3 years ago

Read 2 more answers